Einstein’s special relativity is sometimes popularized with statements like: “moving clocks run slower than stationary clocks and moving rods are length contracted relative to stationary rods”. The problem is that special relativity also states that there can be no absolute motion; so how can one define “moving” and “being stationary”?
The usual answer is that all motion is relative and you can take any inertial frame and declare it the “reference frame” against which all other motions can be measured. This however cannot mean that all other inertial frames, moving relative to this one, must now have slower clocks and contracted rods.
To illustrate this, consider two flashes happening at the same spot, one after the other, say with a ten seconds interval as timed in the reference frame. Two identical vehicles happen to pass in opposite directions, just as the first flash occurs. Assume that the vehicles maintain identical (but opposite) speeds and the occupants measure the distance traveled and the time it took before the second flash was observed (seen). Because light travels at the same speed in all directions in every inertial frame, the observers in the vehicles must get the exact same results.
Now the dilemma: The two vehicles were moving relative to each other and special relativity predicts that their clocks and rods must behave differently due to their relative speed. However, if the vehicles would stop and the occupants compare results, they will find that, within experimental error, they recorded the same distances and the same times.
At ordinary road speeds, this is probably an impractical experiment – the errors will be larger than the effect being looked for. Put the same experiment in space, with ultra fast spacecraft and ultra sensitive equipment, and the results must be identical.
For the scientists out there: how do you explain this apparent paradox in special relativity?
SL: Your Aerospace Watchdog
Fred wrote:
It is exactly this sort of statement (using the vague term “sees”) that causes a lot of confusion. “Observe” would be the better term, in which case there is no such thing as the “stay-home twin aging much more rapidly during the turn-around period”.
The easiest way to do such observation is for the stay-home twin to have laid out a set of equidistant clocks, all synchronized to his own clock. Sister can then read off twin-brother’s aging directly from these clocks as she passes them and she will observe him to age gradually and always faster then herself, for as long as she is moving relative to his frame.
Like Fred, I’ll stay out of the debate between Burt and the ‘rockinggoose’.
SL: Your Aerospace Watchdog
Scruffy writes:
That probably needs a little clarification.
Burt and Christopher led me to rethink the situation in circumstances where acceleration effects are so low that the gravitational redshift is negligible, and we only need to consider the effects of special relativity–especially the degree of mis-synchronization of the clocks as the twins get farther apart.
That is why the adjective “direct” is important in Scruffy’s statement.
But the fact that only one twin experiences acceleration is, of course, a crucial distinction. So the fact of acceleration plays a role even if the value of the acceleration is so small that we can neglect it in comparing clock rates.
At the close of a long comment above, I write why the explanation described in that comment satisfied me:
My reference in that statement is to the fact that I was trying to analyze the way the age difference accumulates as viewed by each twin.
The stay-home twin sees the age difference increasing monotonically, while the traveling twin sees the stay-home twin aging more slowly during the periods of coasting, but aging much more rapidly during the turn-around period. When they finally meet again and are at rest with respect to each other, they compare wristwatches. Each measures the same net difference in age for the period of separation, and neither is surprised at the other’s result.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
Hi rockinggoose, you wrote:
“I’m afraid Burt’s version of the rockets & string scenario in which Scruffy can find no flaw, is hopelessly flawed. I also notice that the notion of the rockets staying at fixed distance “by definition” [ what definition ?, from where ? ]”
OK, let’s stop beating around the bush and show us the relativistic math that proves that the centers of mass of two identical (line astern) rockets with identical accelerations relative to the original inertial frame (hereinafter the ‘reference frame’), starting simultaneously in the reference frame, do not stay at a fixed distance apart in the reference frame. I’ll bet on it that you can’t give rigorous prove for that, but prove me wrong.
By mathematical definition, identical accelerations (dv/dt), starting simultaneously, result in identical velocities at any reference frame time. Identical velocities mean zero relative velocity, yielding unchanging separation in the reference frame. This is true for Newtonian as well as relativistic dynamics.
You must remember that the two rockets do not comprise a single object that Lorentz contracts – they are forcefully held at the same acceleration in the reference frame. In fact, if your position is that the separation (distance in reference frame) between the nose of the trailing rocket and the tail of the leading rocket contracts, it is doubly flawed – the rockets themselves Lorentz contract, so the coordinate distance between the two mentioned points increases, but for simplicity, let’s leave that out of the equations that you are to supply to convince us. (Edit: i.e., assume that the rod/string is attached to the center of mass of each rocket.)
This coordinate distance issue is the crux of our disagreement, so it is fruitless to continue if we can’t resolve it.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt & Scruffy
I’m afraid Burt’s version of the rockets & string scenario in which Scruffy can find no flaw, is hopelessly flawed. I also notice that the notion of the rockets staying at fixed distance “by definition” [ what definition ?, from where ? ] seems to come from Wikipedia ! [The reason Wikipedia is dismissed by academia is because there is zero quality control & anyone whatever their misconceptions can replace the previous content so that the prevailing entries reflect more dogged persistence than enlightened contribution.]
Firstly let’s take a cue from W.Rindler and consider the perspective analogy. If you look down a set of railroad tracks running off into the distance, the sleepers (string) appear to contract with distance (velocity) but the tracks themselves (rockets) “by definition” stay at the same distance. Spot the error in reasoning.
Secondly, contraction is only apparent as clearly stated by Wheeler, Bohm etc. because it is the result of differing simultaneity causing the front to be registered before the rear, from point of view of “moving” frame whilst seeming simultaneous from “stationary” frame. This is the same process as during acceleration, where the objects are smoothly passing through a range of velocities.
That it is certainly not physically real is further shown by using instead the simultaneity of the “moving” frame, where we would obtain increased lengths with increasing velocity so that the moving length gets longer as it accelerates. It just depends on what procedure is used for measurement.
Now let’s consider a statement about relativistic length contraction:
The [rod] appears to be shorter because relativity of simultaneity causes the position of the front [end of the rod] to be marked before the position of the rear [end of the rod].
Now when we replace [rod] by [distance between rockets] and [end of rod] by [rocket] we have a simple and correct statement that the rocket distance also “contracts” when it is measured by the same means as the rod. The last statement is important because Einstein’s theory lays down specific means for synchronising spatially separated clocks and using such synchronised clocks for measuring moving lengths.
Burt’s mistake is to think that there is some other abstract way of determining length during acceleration without measuring it. In effect he’s claiming that the rockets stay at the same distance in Newtonian terms whilst reserving relativistic effects for the string.
If one were to say that “by definition” the proper length of the string remains constant (as is the case), we can see that the “argument” tacitly allows relativistic measurement shortening to act on the string, while for no rational reason witholding it from the inter-rocket distance, for which the same “relative simultaneity” would in fact shorten the measured distance.
Also Scruffy is under a common misconception that the “Twin Paradox” requires acceleration for its resolution. It has been pointed out many times that this is not so. It has got nothing to do with acceleration.
Not only can the period of travel be indefinitely extended before turnaround to render the effect negligable, but also if clocks are used instead ( and more accurately !) a third identical clock can be supposed to be incoming from a distance and be synchronised with the outgoing clock at the moment they pass, thus carrying the time back without any acceleration being involved.
Hi SL, good to hear from you again.
You wrote: “How do you reconcile the two perspectives? As rockinggoose said, you can’t have it both ways! :p”
What both ways? There is no difference between the “realness” from a measurement point of view – time dilation and length contraction are ‘real and measurable’ effects in both cases. The acceleration is just a “crutch”, so to speak, in order to be able to measure time dilation and length contraction more or less independently from simultaneity.
In the ‘rockets and rod’ case, we replace the conventional synchronized clocks and standard meter sticks with directly measurable identical accelerations (of arbitrary magnitude), lasting for identical times in the reference frame. So, the acceleration is not the issue, it is velocity time dilation and length contraction that count, ‘real and measurable’.
Just as real and measurable as the fact that “Bell’s string” would break!
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Burt, I can find no flaw in your “rockets and rod” conclusion, but it brings up an interesting issue:
Just like the in the ‘twin paradox’ where the age difference only becomes ‘real and measurable’ when acceleration enter the scene, it appears that length contraction also only becomes ‘real and measurable’ when acceleration is present.
When acceleration is absent, it seems to me that both effects are due to simultaneity definitions that differ. As you noted, there is no simultaneity issue in the “rockets and rod” from the perspective of the reference frame. Neither is there any simultaneity issue when the traveling twin comes back to her brother – they can both read each other’s clocks directly.
However, you seemed to have convinced Fred above that acceleration does not play a direct role in the aging (or not) of either twin. How do you reconcile the two perspectives? As rockinggoose said, you can’t have it both ways! :p
SL: Your Aerospace Watchdog
Hi rockinggoose, you wrote:
“Why have you avoided answering my obvious question about what difference you surmise to exist between the constant velocity metre rod “contracted” to 90% and one I accelerate up to the same velocity where it will also appear as 90cm ?”
Hmm…, maybe this offers a way to finally settle the Bell ‘paradox’ issue. Do you agree with the following variant, based on your question:
The relativity of simultaneity does not enter into this argument because the simultaneity definition of the reference frame has not changed. What observers in the reference frame measure is ‘real’, as T&W and Thorne argued. For those observers, the rod had to be stretched by the rockets in order to stay attached to both.
I’m prepared to continue with this discussion only if we can concentrate and hopefully agree on the outcome of the above scenario, one way or the other.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
Hi Burt
You couldn’t be more wrong ! I’ve already pointed out that acceleration makes no difference to the reciprocal nature of contraction, and therefore its physical reality. The next two sentences you omitted in the extract you used from my quote state explicitly that the contraction is only “apparent” [their word] and purely a result of relative simultaneity affecting the process of measurement.
Why have you avoided answering my obvious question about what difference you surmise to exist between the constant velocity metre rod “contracted” to 90% and one I accelerate up to the same velocity where it will also appear as 90cm ?
The apparent contraction is in SR simply the result of relativity of simultaneity causing the front end to be registered slightly before the rear end as judged by an observer riding on the rod, whilst they may be “simultaneous” in the different frame of the “stationary” observer.
You seem to forget that if simultaneity in the “moving” frame is used instead, as in the train carriage with a firecracker at each end detonated from the centre leaving soot marks further apart than the original[ proper, normal, or stationary ] carriage length. They would also get further apart as the train accelerated.
As far as the Lorentz transformations go, acceleration is merely change in velocity and at each instant the “contraction” relating to that velocity is reciprocal and apparent.
As David Bohm says: Instead of assuming they are real ie. structural changes in length and duration owing to motion, Einstein’s theory involves only apparent changes, and these are independant of the microscopic constitution….Unlike real changes, these apparent phenomena are reciprocal.”
Or Wolfgang Rindler:
“Relativistic effects are comparable to perspective effects….Moving lengths are reduced, a kind of perspective effect. But of course nothing has happened to the rod itself…” and Rindler goes on by saying that the effect is real – thus showing that the use of the word “real” [by him and others] is not meant to be thought “physically real” but just that the apparent shortening is a real measurable effect.
It’s no good trying to claim that acceleration is “different”. Do you really suppose that Wheeler, Bohm, Rindler and others simply forget to mention such a striking fact ? Have they overlooked mentioning it ? Where, in any book, have found such a phrase as “Oh, by the way, this constant motion contraction is not to be confused with that resulting from acceleration which is no longer reciprocal etc.” ?
I think the opinion of world acknowledged authorities like Wheeler, Thorne etc. is rather more reliable than that of relative unknowns from obscure institutions. The absence of formal refutations is not confirmation of veracity, and I’m surprised that you should suggest this. Physicists have got better things to do, ie. have neither the time nor inclination to search the internet for half-baked articles of which to write formal rebuttals. There’s just way too much dross out there. [I notice Nicolic has also written proposing black holes do not evaporate, but I doubt if black hole theorists are rushing to submit formal refutations.]
You also say Mallinckrodt and Nicolic are “essentially saying the same thing”.
Have you actually read them ? Nicolic is proposing a pulled rod contracts faster than a pushed rod, which has got nothing whatever to do with Mallinckrodt’s slides proposing (among other things) an event horizon related to acceleration. [He also consigns himself to a tiny minority with his title – What ? do you mean to say hardly anyone else realised these things in only a hundred years !]
Hi rockinggoose, you wrote:
“I think you’ll find that what I said does indeed follow from the quotes I gave. ”
I don’t think so! Those quotes have nothing to do with accelerated systems.
“Although it’s true that acceleration can always be distinguished from inertial motion, that does not mean that there must be two types of contraction – one absolute involving mysterious forces somehow “pulling the object together” along its motional direction; and another relative type that is perfectly reciprocal. I know of no text that makes such a claim. ”
Who said anything about “mysterious forces somehow pulling the object together” apart from yourself? In accelerated systems it is the original inertial frame of reference that observes the length contraction of the accelerated rod. In the rod-frame, its length remains constant (if assumed to be perfectly rigid).
However, in the Bell spaceship ‘paradox’, the two identically accelerating ships remain at constant separation in the inertial reference frame (by definition, i.e., identical coordinate accelerations and speeds at all times). If the string was only attached to the leading ship, the inertial reference frame will observe it to Lorentz contract. To remain attached to both ships, it must be physically stretched to a longer proper length.
If we analyze the situation from the rod-frame’s point of view, the leading ship pulls away from the trailing ship. Although their coordinate accelerations are the same, their proper accelerations differ (see Prof. John Mallinckrodt’s presentation: “Simple, Interesting, and Unappreciated Facts about Relativistic Acceleration”). The unattached string remains at constant proper length, but the moment it is attached to both ships, it is stretched. No paradox. And nothing shrinks in absolute terms; something is however stretched in absolute terms in Bell’s scenario.
If we cannot agree on these standard relativistic interpretations of accelerated frames (including Nikolic’s paper), it is a waste of time to argue in circles around it.
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
PS: any luck in finding a formal debunking of Nikolic’s paper? (and Mallinckrodt’s presentation, for that matter, because they are essentially saying the same thing).
Hi Burt
I think you’ll find that what I said does indeed follow from the quotes I gave. Although it’s true that acceleration can always be distinguished from inertial motion, that does not mean that there must be two types of contraction – one absolute involving mysterious forces somehow “pulling the object together” along its motional direction; and another relative type that is perfectly reciprocal. I know of no text that makes such a claim.
That the contraction “is not due to any forces” supports the perspective analogy and rules out the appearance of tension in the string scenario. Since T&W make it clear that contraction is of the measurements due to relative motion affecting simultaneity of the measuring process, it follows that two identically accelerating rockets will exhibit a contracting distance just like any object.
Your use of Michelson-Morley is incorrect. The Lorentz-Fitzgerald contraction hypothesis was to explain the M-M null result when the wave theory of light would predict back and forth time should exceed side-to-side and cause a fringe shift. Einstein introduced the constant to-and-fro speed of light instead as a starting hypothesis so that “real” contraction (of the interferometer) was no longer necessary – indeed to include it as well would reintroduce a fringe shift prediction.
The “proper” length of a rod is its real physical length and this does not change regardless of whether the rod increases in speed or the observer does so. The reciprocation of the contraction in SR is independant of which accelerates.
Consider an an inertially moving metre rod that measures say, 90cm according to us. If we now take our metre rod and accelerate it up to same speed it will also measure 90cm, but what you are suggesting is that there will be some difference in the moving frame between the two rods because one was “accelerated” and the other not !
Although measurements give the appearance of contraction in SR, the proper length remains unchanged and therefore the acceleration and the “inertial” force associated with it must be constant along the length.
Furthermore, in SR the contraction is independant of whether the rod is pushed from the back, pulled from the front or propelled from any other point along its length.
If “real” physical contraction is assumed (departing from SR) then you immediately have problems deciding for instance for a non-uniform rod where most mass is in the front or back half, whether contraction takes place around the geometric centre or the cenre of mass ! Without any “dynamical” theory of contraction, such questions are insurmountable.
What Nicolic does is define an acceleration for the point x at the front or at the rear, from which it seems the rod will “contract” forwards or backwards respectively towards the point of propulsion. Thus the bulk of the rod when back propelled will have slightly lower instantaneous velocity than when front propelled, and thus have a slightly lesser “contraction”. To put it another way the length will seem to contract “quicker” when pulled than when pushed.
All this is wrong, however, for two reasons:-
First the “real physical” contraction is outside SR so it’s misconceived from the outset, and
Secondly his assumption that contraction happens toward the propulsion point is not justified. Imagine a typical NASA type rocket undergoing “real physical” contraction – it is not realistic to suppose all the rest of the rocket contracts towards the engine unless you define it so. The only reasonable assumption for such a non-SR scenario would be contraction about the centre of mass, otherwise you run into problems with conservation of energy.
Hi rockinggoose, you wrote:
Note that he effectively says the contraction is “real” as far as can be measured and caused by “the peculiar nature of space and time. ” How else would the Michelson-Morley null result be interpreted? Also note that Thorne did not speak of accelerated frames here…
You quoted Taylor & Wheeler:
To which you commented: “It follows from their description that proper acceleration does not change linearly along the length of an accelerated rod. ”
I would like to learn how you find what you wrote to follow from the T&W quotation. I’m pretty sure that Wheeler will not agree with you! Your example using perspective ‘contraction’ also has nothing to do with accelerated rods. Perspective may be similar to inertial frames in relative motion, meaning it is a reciprocal ‘contraction’ effect as viewed by either observer. An accelerated frame cannot be exchanged for the inertial frame to obtain reciprocal effects, because (proper) acceleration is absolutely measurable. One frame accelerates and the other one not.
On Nikolic’s paper, you wote:
Whose authoritative opinion is that? Did you find a proper debunking anywhere? You were quoting the authorities Thorne and Wheeler, although the quotes were somewhat irrelevant to the accelerated rod problem. H. Nikolic is also a highly regarded physicist, with lots of publications in respected journals.
The accelerated rod is not contracting in its own frame of reference, but rather as measured in the inertial frame. At the same time, the two rockets are accelerating identically relative to the inertial frame and stay a constant distance apart, while the rod (string) contracts in that frame, so how can it not be stretched? Contraction may not be ‘real’, but that stretch is a real physical effect, applying a force to the string, just like tidal gravity stretching is a real physical effect.
With all that said, SL’s thread does not deal with accelerated frames, but only inertial frames. There, the contraction effects are more slippery and hard to understand. However, there is always the Michelson-Morley type of interferometer test that says something about the ‘realness’ of the contraction – how can there be no difference in the two-way times along the two orthogonal arms if the one arm does not contract?
Regards,
Burt Jordaan (www.Relativity-4-Engineers.com)
May I suggest that close attention is paid to the quotes I included from Kip Thorne and Taylor & Wheeler ( that’s John Archibald Wheeler ) that make it quite clear that the contraction in Einstein’s SR ( as contrasted with Lorentz-Fitzgerald ) is not a physical contraction but an aspect of measurement between relatively moving frames connected with the different simultaneity with which endpoints are recorded.
I particularly chose those quotes among others because J.A.Wheeler is about the most respected authority in the field of relativity and Kip Thorne is another as well respected as any I could think of.
It follows from their description that proper acceleration does not change linearly along the length of an accelerated rod. I included the D’Inverno quote to highlight the fact that misleading and incorrect information did not arrive only with the internet but was always present here and there in published material.
Nicolic’s paper is a not uncommon example (especially on the internet) of erroneous work produced by somebody who has either not properly understood SR, and/or has failed to appreciate the important difference between it and Lorentz’s theory.
To show the kind of error of reasoning involved, let me use the analogous perspective “contraction” due to distance.
If I have a horizontal line on the ground, then objects will “contract” in dimension as they move away perpendicular to the line, in propertion to distance. The effect is reciprocal.
Suppose two people 20 yards apart along the line, hold a cotton thread taut between them and each marches perpendicular to the line in the same direction.
Since I “know” that the thread will contract, and I also reason that the two people are moving parallel and therefore maintaining the same distance, then it follows that the thread will be stretched until it breaks, right ?
If we use the right hand end as a reference, an object seems to contract from the left, and vice versa, with the LH end as reference, contraction happens from the right.
So with an accelerating rod, if we use the forward end as our reference, it could seem that contraction is in the direction of motion from the back end, which we could (wrongly) deduce will have a slightly higher acceleration than the front.
Similarly if we use the back end as reference point, contraction “seems” to occur against the direction of motion from the front end.
Thus if we persist (contra to Wheeler & Thorne) in regarding the contraction as real physical shrinkage we not only are misled into thinking that acceleration changes along the rod, but that pushing a rod from the back is in some way manifestly different from pulling it from the front. This may be an interesting aspect of the old Lorentz theory but it has no place in Special Relativity.
rockinggoose wrote:
“Also far from being “undisputed”, the Nicolic paper is simply wrong, as you can easily verify yourself.”
I would be interested to know of any formal paper disputing (debunking) the Nikolic paper. I have in mind something more technical than the (technically flawed) reasoning that you supplied. You seem to have missed the meanings of those equations (21 and 23). They give different results, which represent the length contraction profiles as viewed in the original inertial frame. As shown in figure 1, they are for the cases where the constant acceleration is applied to the back end and front end of a rod respectively. If SR is right, then those results are perfectly correct.
“Therefore the main “result” of the paper is a trivial co-ordinate change !”
Proper acceleration changes linearly along the length of a rod accelerated lengthwise. This explains why the result has the appearance of a simple coordinate change, while it is not. When the rear end is accelerated at a, the front end accelerates at a_f a. This is stock-standard SR. One cannot dispute it without disputing SR.
Burt Jordaan (www.Relativity-4-Engineers.com)
I think it should be made clear that there are two distinctly different theories: Lorentz’s and Einstein’s. In the former, contraction is due to velocity with respect to an absolute space and is a real physical shrinkage that could cause mechanical tensions that could for instance break strings etc.
In the latter, contraction is an effect of the measurement process itself and thus has no physical effect on the object itself.
It is not consistent or acceptable to use a “pick’n’mix” combination of the two theories whereby you have two different types of contraction, one for constant motion and another for acceleration. Within each theory there is just one process of contraction and it arises differently in the two theories.
For the “standard” SR view, let’s hear from Kip Thorne:
“This was the contraction inferred by Fitzgerald, but now put on a firm foundation: The contraction is caused by the peculiar nature of space and time, and not by any physical forces that act on moving matter.”
And in Taylor and Wheeler we find:
“Is the contraction real or apparent ? We might answer this question by posing a similar question. Is the frequency, or wavelength, shift in the Doppler effect real or apparent ?…..When the source and observer are in relative motion, the observer definitely measures a frequency (wavelength) shift….The effects are real in the same sense that the measurements are real. We do not claim that the proper frequency has changed because of our measured shift….The effects are apparent (that is, caused by the motion) in the same sense that proper quantities have not changed.”
“We do not speak about theories of matter to explain the contraction but, instead, we invoke the measurement process itself.”
“Since length measurements involve the comparison of two lengths….we can see that the Lorentz length contraction is really not a property of a single rod by itself but instead is a relation between two such rods in relative motion.”
Nevertheless some authors seem to be confused, like Ray D’Inverno, author of a well known book on relativity, who writes (on page 33):
“In an attempt to explain the null result of the Michelson-Morley experiment, Fitzgerald had suggested the apparent shortening of a body in motion relative to the ether. This is rather different from the length contraction of special relativity, which is not to be regarded as illusory, but is a very real effect.”
Whatever view one takes of the “reality” of the measured contraction in SR, D’Inverno’s statement is quite wrong in regarding Fitzgerald’s contraction as less real than SR when it was in fact an absolute physical shrinkage of the interferometer that was hypothesized to explain The M-M null result.
No, this is wrong. If we are dealing strictly with standard SR then the whole concept of relativistic contraction is an effect of the measurement and therefore, not being physically real, cannot break strings etc. That acceleration is a vector has got nothing to do with it. There is no reason to suppose that the rockets will “pull away from each other”. This is merely a fanciful “reversing” of the “real Lorentz contraction” following the dubious “parallel trajectory” assumption I mentioned.
Now I realise that we would all like to believe that our views are “mainstream” views but I’m afraid that in this case there is plenty of divergent opinion. The originators of the problem were contradicted at the time, Bell (remember he disdained Einstein’s SR in favour of Poincare-Lorentz ) had all the CERN theorists against his view, and a recent resurrection of the problem in a Japanese journal was strongly opposed within the academic community.
Also far from being “undisputed”, the Nicolic paper is simply wrong, as you can easily verify yourself.
Look at the crucial equations (21) and (23) which represent the distinct scenarios. In fact they are the same equation ! All that has happened is that in one the rod is represented as from x-L to x whereas in the other it is represented as from x to x+L as you can easily check by substitution. Therefore the main “result” of the paper is a trivial co-ordinate change !
Hi Rockinggoose, you wrote:
“Some people favour one side, some the other and some withhold commitment, but there isn’t necessarily a “modern” view – and furthermore, even if a “modern view” were to adhere to string breaking, such would be to assert the absolute physical reality of the contraction and hence reject the reciprocal nature of SR.â€
The accelerating rocket problem is obviously not reciprocal. The standard SR interpretation says that the string will break, because the leading rocket will pull away from the trailing one. Acceleration is a vector and has an absolute direction, so there is never any doubt as to which one is leading.
You later wrote:
“In the rocket and string problem the crucial assumption in deducing string breaking is that since the trajectories must be parallel then any later distance must be the same as the starting distance. But we must distinguish between measurement and deduction here. â€
In this particular case, with constant and equal proper acceleration for both rockets, the separation in the inertial reference frame remains the same, but the proper distance between the rockets increase and hence the string breaks. I do not know of any mainstream relativist that disputes that analysis.
“ As I said before, the issue of string breaking depends on the very issue of this blog, ie, the “reality” of relativistic contraction; and opinion on that is as divided as it ever has been. â€
I think SL had the non-accelerated case in mind, where simultaneity plays a big role in the analyses. The accelerated case is not quite a GR scenario, as Fred seems to hold, but can be totally solved within SR. However, simultaneity becomes a thorny issue in accelerated frames of reference.
Apart form the reference that SL quoted, another accessible treatment of the (rigid) accelerating rod is H Nicolic: http://arxiv.org/abs/physics?papernum=9810017. Many analyses of the Bell spaceship paradox are based on this undisputed paper.
Burt Jordaan (www.Relativity-4-Engineers.com)
Rockinggoose honks, “In the same way if the contraction in relativity is not physically real but a measurement effect,…”
That gets us back to the beginning of this thread when we struggled to define the term “physically real.”
What is reality other than what we measure?
The reality is that A measures B’s meter sticks to be foreshortened and B measures A’s meter sticks to be foreshortened. Likewise, each measures the other’s clocks to run slowly and to be out of synchronization.
Though that reality boggles the mind of one whose instincts are forged in a non-relativistic environment, it is completely consistent with the laws of physics that both observers agree upon.
When you start to discuss the rocket and string problem, you introduce both the properties of materials and relative acceleration. The latter moves us out of the realm of special relativity and requires a general relativistic analysis.
In any case, it’s clear that whether the string breaks or not, both observers will agree about that fact, and it will be consistent with the laws of physics and the properties of the materials involved. If we assume that each observer is a good physicist and applies the properties of materials and the laws of mechanics properly, then each should predict the result correctly.
With that, I’ll hop back to the sidelines.
Fred Bortz — Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)
In the rocket and string problem the crucial assumption in deducing string breaking is that since the trajectories must be parallel then any later distance must be the same as the starting distance. But we must distinguish between measurement and deduction here.
Let’s take the common analogy of “perspective” for the contraction whereby objects shrink as they get further away rather than getting faster.
If I’m on a platform and a distant railway carraige looks or measures shorter than a nearby one I can project a perpendicular at the rear of the near carraige that will graze the rear of the distant one. I can also move to the front and construct another perpendicular that grazes the front of both. I can thus deduce that the end-to-end distance has not “really” reduced for the far carraige.
But my direct measurements with say, a tape measure held in front of me will still show the contraction of perspective.
In the same way if the contraction in relativity is not physically real but a measurement effect, it will apply to the rockets as well, and a “deduction” based on “parallel” trajectories will not change the situation, just like the deduction from perpendiculars does not affect the measured perspective.
As I said before, the issue of string breaking depends on the very issue of this blog, ie. the “reality” of relativistic contraction; and opinion on that is as divided as it ever has been.
The header of this thread is “Is Einstein’s time dilation and length contraction real ?” Leaving aside the grammatical error I would like to point out that this debate has continued for over a century.
The positions are that the Fitzgerald-Lorentz contraction first hypothesized to account for the Michaelson-Morley expt. has always been regarded as an absolutely real physical shrinkage, whereas the SR contraction, because among other things of its reciprocal nature, has generally been regarded as “apparent” or an effect of measurement. This is because it is obviously impossible, not to say absurd, to suggest that:
length A < length B whilst length B < length A, whereas of course, to say that A's measurement of length B < length A is perfectly compatible with the condition with A & B reversed.
Now in the rocket string problem it is clearly the case that:
"Real" Lorentz-Fitzgerald contraction means the string breaks but…
If "measured" SR contraction is not physically real it means the string does not break.
Some people favour one side, some the other and some withhold commitment, but there isn't necessarily a "modern" view – and furthermore, even if a "modern view" were to adhere to string breaking, such would be to assert the absolute physical reality of the contraction and hence reject the reciprocal nature of SR.
Rockinggoose wrote:
The modern view can easily be derived from this easy-read presentation by dr. John Mallinckrodt of Pomona university. It deals with the acceleration of a rigid rod, but it is easy to deduce from it that if the rockets accelerate identically, then according to standard special relativity, the string must stretch.
For the string not to stretch, the front rocket must accelerate less than the rear rocket, just like the case of the two ends of the rigid rod.
Either you accept special relativity and conclude that the string must stretch, or you are effectively rejecting special relativity.
http://www.csupomona.edu/~ajm/professional/talks/relacc.ppt
SL: Your Aerospace Watchdog